Estimating and detecting the 3D location and orientation of objects is a classic problem. Numerous prior art systems have issues which negatively influence the achievable size, weight, and power, cost and precision of object 3D localization and orientation.
A fundamental issue with prior art optical digital imaging systems shown in FIG. 1 (upper drawing) that perform 3D localization is that resolution is related to the spatial density of image sensing pixels: specifically, pixels with fixed system geometries limit higher precision. In general prior art digital imaging systems, when the lens is at its maximum diameter, the image size formed behind the lens, for particular sized pixels, is a maximum; and put another way, the space-bandwidth product (SBP) at the image plane is a maximum. With smaller diameter lenses, but with a constant marginal ray angles or F/#, smaller images are captured and the system's SBP is reduced. But as the lens diameter decreases, the image size becomes so small that for general scenes, all object information is not captured in sufficient detail.
Similarly in prior art measurement systems as shown in FIG. 1 (upper drawing), the baseline B between sensors determines the SBP, and hence precision of estimating x, y, z values for object 105 in system 100. Optics 110a and 110b, with focal lengths fa and fb, respectively, form images of object 105 at distances ya and yb, respectively, from the optical axis on their respective sensors 120a and 120b. The estimates of distances ya and yb determine y location and ratios of fa/ya and fb/yb determine the range, thus a more dense sampling at sensors 120a and 120b increases the precision of the estimations—but at the cost of higher size, weight and power.
Like the two elements of a stereo imaging system shown in the upper drawing of FIG. 1, prior art radar systems (see lower drawing of FIG. 1) also use arrays of detectors to detect objects in 3D space. Radar systems code across each element of a multi-element antenna array in order to detect/localize/reject, etc. targets in a 3D space in the presence of unknown noise and clutter. The number of antenna elements does not theoretically limit the potential angular estimation accuracy, except through SNR.
The main differences between the radar system (lower drawing) of FIG. 1 and the optics system (upper drawing) of FIG. 1 is related to the fact that typical radar wavelengths can be temporally coherently sampled with antenna 102a, 102b, to 102n. In radar systems, the antenna elements are arranged so that the field patterns from each element overlap. Mathematical weights 104a, 104b, to 104n are applied across the array elements or channels and then summed 106 to determine the output signal squared 107. The weights can be deterministic, such as Fourier coefficients, or can be a function of the sampled data, such as used in Auto-Regressive (AR) modeling, and can have a representation on the complex unit circle 108 in FIG. 1 where both signal amplitude and object angle can be represented.